Bird is away from this fly (6)
I believe the answer is:
thrush
'bird' is the definition.
(thrush is a kind of bird)
'is away from this fly' is the wordplay.
'away from' is a deletion indicator.
'fly' becomes 'rush' (fly can mean to rush around).
'this' with 'is' taken away is 'th'.
'th'+'rush'='THRUSH'
(Other definitions for thrush that I've seen before include "Mouth fungus or songbird" , "Common songbird or throat infection" , "Songbird with brownish back and speckled breast" , "Singing bird or mouth-troat infection" , "Brown songbird" .)